# Theory of Failure for Ductile Materials

(previously posted on alt.mechanical.engineeing)
I've been doing some bolt stress analysis recently and came across the
following issue:
Following the methods taught by Shigley we typically use the maximum principal stress theory of failure to judge whether or not a bolt will break when it is being tightened.. The plane stress state in the bolt during tightening consists of tension and shear. I calculate the max principal stress and compare it to the ultimate strength of the bolt to determine my design margin. However, at my company we use a lot of 300 stainless steel screws that are basically in the annealed state (80ksi ultimate and 30 ksi yield). In actuality the screws probably get work hardened during heading and thread rolling but the specs say they don't. So, I have to assume I have very ductile fasteners. In reading Shigley he justifies max principal stress by saying it only applies to high strength bolts (SAE grade 3 or higher?) that behave like brittle materials (no appreciable yield before fracture). I went back and re-read the section on theories of failure and, sure enough, max principal stress is only recommended for brittle materials. It isn't "safe" for ductile materials because it assumes the material is as strong in shear as tension. That leaves me with max shear and max distortion energy (von Mises Hencky). These theories are recommended for ductile materials with max shear being the most conservative. My problem is that I want a theory of failure that applies to *fracture* of ductile materials. Max shear and max distortion are only recommended for determining the onset of yield. I don't care if my 300 stainless screws undergo a little plastic deformation (strain hardening?) as long as they dont break off.
Any suggestions?
Al
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Aldo wrote:

The Maximum normal stress theory (max principal stresses) is more conservative (extra safe) for metals. It will show lower margins of safety (or calculated safety factors) than other failure theories such as Von Mises (DET).

Just do the checks in NASA's Criteria for Preloaded Bolts, NSTS-08307A. http://mmptdpublic.jsc.nasa.gov/mswg/Documents/NSTS%2008307.pdf
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>

break
No - "ductile materials that behave like brittle materials"
There are brittle materials and there are brittle behaviors (failure), and the two are totally different concepts- common ductile materials like steel and aluminum can and do regularly fail "brittle-ly" (in a brittle fashion) .
Published material test parameters are from tests done at a given rate of application at a given temperature and with a single (usually axial) stress applied to a test specimen.
That same material which failed in a ductile fashion on the test machine can fail in a brittle fashion in low temperatures (e.g., many steels and plastics), they can fail in a brittle fashion a high rate of force application ( e.g., some aluminums and plastics), and they do fail in a brittle fashion in certain ratios of combination (biaxial and triaxial/tension-compression-shear) stresses. And in combinations thereof.

distortion
*fracture*
for
Bascially, published test results must be viewed as only applicable in a limited real world contexts, and only extended to real-world applications accordingly.
When the application becomes critical as to failure mode, you must either test it yourself using real rates, real temperatures, and real shear and axial stress combinations, and extend your own results to your applications, or find someone with such experience.
----
And, experienced engineers stay below the proportional limit and have learned how to keep it simple - the engineer's job is to provide information as to predictable response of the physical assets of their firm or client. To this end, they use mathematical modeling, i.e., they apply observed conditions to known models (equations). The models (equations) have inherent errors, and the engineers assumption of applicability of that equation has explicit errors. Bad enough we have the assumption-of-applicability errors - no need to compound the reliability of the chosen applicablility by using something so variable as the shaky equations in the area above proportionality.
Using simple reliable equations is a better use of the firm's assets (including engineering time) than using cumbersome equations that are less rigorous and predicatble in their real world application of the end product.
-----------
BTW - Note that many equations we use are actually derived from experiment, and as "best-fits", they have inherent errors. (I mention this because the complex tensile region equations have only a very narrow real world reliable use. The standard "first derivative of an equation to get the error rate" shows that in spades.)
In my library, I have a book that lists the probability of error of many engineering equations. The range is from 10% for most of the common engineering equations up to 100% (yes, 100%) for autofrettage of cannon cylinders. (That 100% means you can have half as much pressure as the equation predicts is necessary to do the job and you fell short, or you can have half again as much pressure as the equation predicts is necessary to do the job and you either wasted a lot of energy or it blows up. IMHO, that kind of range indicates a rate-of-application-parameter not considered by the common autofrettage equation.)
(And - I did not pick the 100%, so don't ask me if it should have been 50%. As I read it, the range of error, say X %, is applied at its midpoint value to the value found by the equation, say X - thus, the possible error is between X/2 and 3X/2 - a range of X, i.e., 100% of the equation value. )
fwiw -
(I think I got it ok... anyway, as they say - you get what you pay for.. )

<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>

## Site Timeline

• ### Multivariable Calculus 4th edition by Stewart Dan Clegg Barbara Frank

• Share To

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.